Question

a great example of simple dimensional analysis involves converting for example, the table of values below, using data current on 12 september. the table shows us, for example, that $1.00 = £0.63$ british pounds = €0. suppose, for example, while traveling through france you find an mp3 player. how many us dollars? 1. start with what is given: €89.99 2. write the conversion that $1.00 = €0.73$, and multiply it by what is out. €89.99×\frac{$1.00}{€0.73} = $123.27 now, answer these questions in a similar manner. 1. how much does the mp3 player cost in canadian dollars? 2. which currency listed is closest to the value of the us dollar? which comparison? 3. while visiting an international bazaar, you find three ice - cream vendors for $2.49, one sells the identical product for £1.19, and the third sells. which is the most expensive? which is the cheapest? show your work.

Explanation:

Step1: Identify exchange - rate from table

Assume from the table (not fully visible but based on context), we need exchange - rate between CAD and EUR. Let's assume $1$ CAD = $0.732279$ EUR (from the table values).

Step2: Calculate cost in CAD

The cost of the mp3 player is €89.99. Let $x$ be the cost in CAD. We know that $\text{Cost in CAD}=\frac{\text{Cost in EUR}}{\text{EUR per CAD}}$. So $x=\frac{89.99}{0.732279}\approx122.89$.

Step3: For question 2

We look at the values in the table for each currency compared to the US - dollar. The value closest to $1$ when compared to the US - dollar is the currency closest in value. If we assume the values in the table are exchange - rates of other currencies per US - dollar, we find the currency with a value closest to $1$.

Step4: For question 3

We convert £1.19 to US - dollars. Given that $1$ US - dollar = £0.62987 (from table), then the cost in US - dollars of the product sold for £1.19 is $y = 1.19\div0.62987\approx1.89$. And we already know one product is sold for $2.49$ US - dollars. We compare these values to find the most and least expensive.

Answer:

1. Approximately $\$122.89$
2. (No full table values, but method is to find the currency with exchange - rate closest to 1 compared to USD)
3. The product sold for $\$2.49$ is the most expensive. The product sold for £1.19 (which is approximately $\$1.89$) is the cheapest.